Cydney is proving that perpendicular lines have slopes that are opposite reciprocals. She draws line p and labels two points on the line as (0, a)(0, a) and (b, 0)(b, 0) . Enter the answers, in simplest form, in the boxes to complete the proof. The slope of line p is . Rotate line p 90° counterclockwise about the origin to get line q. The labeled points on line p map to (−a, 0)(−a, 0) and ( , ) on line q. The slope of line q is . The slopes of the lines are opposite reciprocals because the product of the slopes is .
Accepted Solution
A:
check the picture below.
with a rotation of 90° from the origin, we get from points (0, a) and (b,0) to the points with equivalent values of (-a, 0) and (0, b). Notice that in the graph we can map those values to a = 4 and b = 6, however, "a" and "b" are just constants and can be any value whatsoever, in this case for the sake of exemplification, they happen to be that.
now, slopes of perpendicular lines, have a product of -1, let's check these ones,